Symmetry Solutions and Reductions of a Class of Generalized (2+1)-dimensional Zakharov-Kuznetsov Equation

被引：15

作者：

Johnpillai, A. G.

Kara, A. H. ^{[2
]}

Biswas, Anjan ^{[1
]}

机构：

[1] Delaware State Univ, Dept Math Sci, Dover, DE 19901 USA

[2] Univ Witwatersrand, Sch Math, ZA-2050 Johannesburg, South Africa

来源：

INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION | 2011年 / 12卷 / 1-8期

关键词：

Generalized ZK equation; lie point symmetries; optimal system; symmetry reduction; group-invariant solutions;

D O I：

10.1515/IJNSNS.2011.003

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, we study a particular class of the generalized (2 + 1)-Zakharov-Kuznetsov (ZK) equation from the Lie group-theoretic point of view. The Lie point symmetry generators of the underlying equation are derived. We obtain the optimal system of one-dimensional subalgebras of the Lie symmetry algebras of the equation. These subalgebras are then used to reduce the underlying equation to partial differential equations (PDEs) having two independent variables. Furthermore, by studying the reduced PDEs utilizing their symmetry properties, we construct a number of symmetry reductions and exact group-invariant solutions to the underlying equation. A conserved density is also retrieved by the multiplier approach.

引用

页码：45 / 50

页数：6

共 8 条

[1] 1-Soliton solution of the generalized Zakharov-Kuznetsov equation with nonlinear dispersion and time-dependent coefficients [J].